As an upgrade for higher fields, a REBCO high-temperature superconductor (HTS) insert coil with a remarkable cold bore of 68-mm diameter has been constructed with the goal to be routinely operated to attain total fields of 25 T and beyond in HOMER II. HOMER II is the most advanced superconducting high-field facility of the Institute for Technical Physics at the Karlsruhe Institute of Technology. With its basic magnet configuration, consisting of NbTi and (NbX) <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Sn low-temperature superconductor solenoid sections, HOMER II can generate a magnetic field of 20 T in a large bore of 185-mm diameter at a Helium bath temperature of 1.8 K. The REBCO HTS insert coil was manufactured using the rarely implemented concept of layer winding technology and consists of five nested solenoids. In this article, we report on the design of the insert, its construction, and commissioning as well as related aspects. In the initial operation period, magnetic fields of up to 26.5 T were obtained at 1.8 K and 24.0 T at 4.4 K, respectively, without training steps and quenching or other problems.